14,353 research outputs found
Captures of stars by a massive black hole: Investigations in numerical stellar dynamics
Among the astrophysical systems targeted by LISA, stars on relativistic
orbits around massive black holes (MBHs) are particularly promising sources.
Unfortunately, the prediction for the number and characteristics of such
sources suffers from many uncertainties. Stellar dynamical Monte Carlo
simulations of the evolution of galactic nucleus models allow more realistic
estimates of these quantities. The computations presented here strongly suggest
that the closest such extreme mass-ratio binary to be detected by LISA could be
a low-mass MS star (MSS) orbiting the MBH at the center of our Milky Way. Only
compact stars contribute to the expected detections from other galaxies because
MSSs are disrupted by tidal forces too early.Comment: 4 pages, 2 figures, to appear in the proceedings of "The Astrophysics
of Gravitational Wave Sources", a workshop held at the University of
Maryland, April 24-26, 200
Don’t Judge the S&P 500 by its Cover: When Expectations Meet Regression
This study aims to answer whether the health of the United States equities market is a representation of the well-being of the macro-economy. There are two primary goals in this study. The first is to model the determinants of fluctuating stock prices in the short-run. For this reason, data is collected in monthly units intended to represent short-term fluctuations in the S&P price over time. The second is to model the expected impact of recessionary pressures on the performance of equities
Algebraic relations between solutions of Painlev\'e equations
We calculate model theoretic ranks of Painlev\'e equations in this article,
showing in particular, that any equation in any of the Painlev\'e families has
Morley rank one, extending results of Nagloo and Pillay (2011). We show that
the type of the generic solution of any equation in the second Painlev\'e
family is geometrically trivial, extending a result of Nagloo (2015).
We also establish the orthogonality of various pairs of equations in the
Painlev\'e families, showing at least generically, that all instances of
nonorthogonality between equations in the same Painlev\'e family come from
classically studied B{\"a}cklund transformations. For instance, we show that if
at least one of is transcendental, then is
nonorthogonal to if and only if or . Our results have concrete interpretations
in terms of characterizing the algebraic relations between solutions of
Painlev\'e equations. We give similar results for orthogonality relations
between equations in different Painlev\'e families, and formulate some general
questions which extend conjectures of Nagloo and Pillay (2011) on transcendence
and algebraic independence of solutions to Painlev\'e equations. We also apply
our analysis of ranks to establish some orthogonality results for pairs of
Painlev\'e equations from different families. For instance, we answer several
open questions of Nagloo (2016), and in the process answer a question of Boalch
(2012).Comment: This manuscript replaces and greatly expands a portion of
arXiv:1608.0475
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